Download Lecture 25 – The Solid State: types of crystals

2P32 – Principles of Inorganic Chemistry
Dr.M.Pilkington
Lecture 25 – The Solid State: types of crystals, lattice
energies and solubility’s of ionic compounds.
1. Types of crystals: metalic, covalent, molecular and ionic
2. Lattice energy
3. Solubility's of ionic compounds
4. Solubility's as a function of lattice and hydration energies
1. Types of Crystals

The realm of inorganic chemistry was considerably expanded in the early 20th
Century when X-ray diffraction revealed information on the structure of solids.

Solids are composed of atoms, molecules, or ions arranged in a rigid, repeating
geometric pattern of particles known as the crystal lattice.

Crystals are usually categorized by the type of interactions operating among the
atoms, molecules or ions of the substance.

These interactions include ionic, metallic, and covalent bonds as well as
intermolecular forces such as hydrogen bonds, dipole-dipole forces and London
dispersion forces.

In the classification of crystals as well as categorizing them by their lattice
types, i.e. monoclinic, cubic, tetragonal etc… we can also classify them according
to their chemical and physical properties. In this respect, we have four types of
crystals, metallic, covalent, (covalent) molecular, and ionic.
1. Metallic Crystals

Metals – elements from the left side of the periodic table form crystals in
which each atom has been ionized to form a cation and a corresponding number
of electrons.

The cations are pictured to form a crystal lattice that is held together by a
“sea of electrons” – sometimes called a Fermi sea.

The electrons of the sea are no longer associated with any particular cation but
are free to wander about the lattice of cations.

We can therefore define a metallic crystal as a lattice of cations held
together by a sea of free electrons.
The sea analogy allows us to picture
electrons flowing from one place in
the lattice to another.

If we shape the metal (copper is a good example) into a wire. If we put electrons
in one end of the wire, electrons will be bumped along the lattice of cations until
some electrons will be pushed out of the other end.

The mobility of the delocalized electrons accounts for electrical conductivity.

Metals are characterized by their tensile strength and the ability to conduct
electricity.

Both properties are the result of the special nature of the metallic bond.
Bonding electrons in metals are highly delocalized over the entire crystal.

The great cohesive force resulting from the delocalization is responsible for the
great strength noted in metals.

The bonding strength in metals varies with the number of electrons available as
well as with the size of the atoms.
i.e. Na – 1 valence electron m.p. 980C
Mg – 2 valence electrons m.p. 6490C
W – 6 valence electrons m.p. 60000C

Metal crystals all have a high density which means that they usually have the
hcp or fcc structure.

Magnesium, scandium, titanium, cobalt, zinc and cadmium have the hcp
structure.

Aluminium, calcium, nickel, copper, palladium, silver, platinum, gold and lead
have the fcc structure.

Alkali metals, iron, chromium, barium, and tungsten have the bcc structure.
2. Covalent Network Crystals

A covalent network crystal is composed of atoms or groups of atoms arranged
into a crystal lattice that is held together by an interlocking network of covalent
bonds.

Covalent bonds (the result of the sharing of one or more pairs of electrons in a
region of overlap between two or perhaps more atoms) are directional
interactions as opposed to ionic and metallic bonds, which are non directional.

For example diamond – each carbon is best thought of as being sp3-hybridized
and that to maximize the overlap of these hybrid orbitals, a C-C-C bond angle of
109.50 is necessary.

Hence the interactions are directional in nature.

Other examples of compounds that form covalent network crystals are silicon
dioxide (quartz), graphite, elemental silicon, boron nitride (BN) and black
phosphorous.

The structure of diamond is based on a fcc lattice. There are 8 C atoms at the
centre of the cube, 6 C atoms in the face centre, and 4 more within the unit
cell. Each C is tetrahedrally bonded to four others. This tightly bound lattice
contributes to diamond's unusual hardness. In graphite each C is bonded to
three others and the layers are held together only weakly.

Covalent crystals are hard solids that possess very high melting points.
They are poor conductors of electricity.
3. Molecular crystals

Very soft solids that possess low melting points.

They are poor conductors of electricity.

Molecular crystals consist of such substances as N2, CCI4, I2 and benzene.

Generally, the molecules are packed together as closely as their size and shape
will allow.

The attractive forces are mainly van der Waals (dipole-dipole) interactions.

Water molecules are held together by directional H-bonds.

Intermolecular forces in this case can either be nondirectional as is the case of
crystals of argon, or directional, as in the case of ice.

In the latter case, the H-O∙∙∙H angle is 109.50, an angle determined by the
geometry of the individual water molecules.

Examples of molecular crystals:
Molecules of Argon gas
H-bonding of water molecules
to form the diamond structure
of ice.
4. Ionic crystals

Hard and brittle solids.

They possess high melting points.



They are poor conductors of electricity, but their ability to conduct increases
drastically in melt.
The packing of spheres in ionic crystals is complicated by two factors :

charged species are present

anions and cations are generally quite different in size
Some general conclusions can be drawn from ionic radii :



within the same period the anions always have larger radii than the cations
the radius of the trivalent cation is smaller than that of the divalent cation,
which is smaller than that of the monovalent cation
It should be realized that the value of any ionic radius only serves as a useful
but approximate size of the ion.. The fact that the ionic radius of Na+ is 0.98Å
does not mean that the electron cloud of the ion never extends beyond this
value. It is significant because when it is added together with the radius of an
anion, e.g. Cl-, the sum is approximately equal to the observed interionic distance.
Formation of an Ionic Crystal – when two elements, one a metal with a low
ionization energy and the other a nonmetal with a highly exothermic electron
affinity are combined, electrons are transferred to produce cations and anions.

These forces are held together by non-directional, electrostatic forces known
as ionic bonds.
A hypothetical view of the formation of
sodium chloride, the constituent elements
are combined, electrons are transferred
and ionic bonds among the sodium and
chloride ions are formed.

Examples of compounds that form ionic crystals are CsCl , CaF2, KNO3, alumina,
Al2O3, zirconia, ZrO2 (very hard).

Cubic zirconia is an imitation diamond, when crystallized it can be used as a jewel
or it can be used as an industrial product for abrasion.
Melting Points of a Class of Ionic Compounds
LiF – 8450
BeO - 25300
NaF – 9930
MgO - 28520
KF – 8580
CaO - 26140
RbF – 7950
SrO - 24300
CsF- 6820
BaO – 19180
2. Lattice Energy
The energy change that accompanies the process in which the isolated gaseous
ions of a compound come together to form 1 mol of the ionic solid.

For a solid composed of monoatomic, single charged ions, such as NaCl, the
lattice energy is the energy corresponding to the reaction shown below:
Na+ (g) + Cl- (g)

NaCl (s)
Energy is released in such a process; the energy of the products is lower than
the energy of the reactants. (Remember exothermic thermodynamic quantities
carry a negative sign).
Theoretical evaluation of Lattice Energy

First we consider the electrostatic interaction within an ion pair made up of one
sodium cation and one chloride anion.

Assuming the energy of the isolated gaseous ions is taken to be zero, the
potential energy of the ion pair is given by Coulomb’s law:
E = (Z+e)(Z-e)/r
where Z+ = integral charge on cation
Z- = integral charge on anion
e = fundamental charge on an electron
r = interionic distance as measured from center of cation to the center
of the anion

If we want the interionic distance to be in Angstrom units and the energy to be in
kJ the exact relationship for Coulomb’s law for one Na+Cl- ion pair is:
E = AZ+Z-/r
where A = 2.308 x 10-21
E = energy kJ
r = interionic distance, Å.




In a crystal we have to sum, all of the ionic interactions in the crystal.
i.e the total Coulombic energy for a Na+ cation must account for all the charged
species surrounding that cation.
For the NaCl lattice, there are 6 anions at a distance of r, 12 other cations at a
distance of √2, 8 anions at a distance of r√3, 6 cations at a distance of 2r and so
forth.
The sum of all of these Coulombic interactions will be the total Coulombic energy
for one sodium chloride cation Ecoul and is given by the following equation:
Ecoul = 6AZ+Z-/r + 12AZ+Z+/r√2 + 8AZ+Z-/r√3 + 6A Z+Z+/2r …
Ecoul = AZ+Z-/r (6-12/√2 + 8/√3 – 6/2 ….)

This series is a constant and depends on the crystal structure

If sodium cations and chloride anions assumed the CsCl or zinc blende structure,
this equation would be different.

These unique series for each crystal structure are known as Madelung constants
(M)
Madelung Constants for Some Common Crystal Structures:
Crystal Structure
Coordination Number
Madelung Constant M
Sodium Chloride
6
1.748
Cesium Chloride
8
1.763
Zinc Blende
4
1.638

Using the symbol MNaCl for the Madelung constant unique to NaCl

Ecoul = AZ+Z-MNaCl/r

We can see that M varies with structure type and that it is higher for higher
coordination numbers

Ecoul is the total Coulombic energy for one sodium chloride cation, assuming that
all of the ions are point charges, charges that act as if they are at the very
centre of the hard spheres representing the ions.

If this is the case then Ecoul would be the lattice energy for NaCl

In reality however, this model must be used with caution as ions are not really
hard spheres, but electrons surrounding a nucleus.

If hard spheres approach too closely to one another, a strong repulsive force will
result and we must also consider the energy of this interaction.
3. Solubilities of Ionic Compounds
For example NaCl
NaCl (s)
lattice energy
Na+(g) + Cl-(g)
H2O
heat of soln
H2O
Na+(aq) + Cl-(aq)

You need to put in energy to get the ions (salt) into ions in the gas phase.

This energy will be recovered when the ions become hydrated.

“high” lattice energy, “low” hydration energy – salt will be insoluble

“low” lattice energy. “high” hydration energy – salt will be soluble.
4. Solubility's as a Function of Lattice Energy and Hydration Energies.
Example 1.
NaF
(s)
Na+(g) + F- (g)
H = +885 KJmol-1
Reverse of the lattice Energy
Na+ (g)
Na+ (aq)
H = -405 KJmol-1
F- (g)
F- (aq)
H = -497 KJmol-1
NaF(s)
Na+(aq) + F-(aq)
H = -17 KJmol-1
i.e. exothermic
G = H-TS
Example 2
CaF2 or fluorite is insoluble in H2O
CaF2 (s)
Ca2+(g) + 2F-(g)
H = 2630 KJmol-1
Ca2+(g)
2F-(g)
Ca 2+ (aq)
2F-(aq )
H = -1592 KJmol-1
H = -994 KJmol-1
CaF2 (s)
Ca
2+
(aq)
+ 2F-(aq)
H = +44 KJ mol-1
reaction is endothermic